Let $A$ be a set.
- The set of transitive relations from $A$ to $B$ is the subset $\smash {\mathrm{Rel}^{\mathrm{trans}}\webleft (A\webright )}$ of $\mathrm{Rel}\webleft (A,A\webright )$ spanned by the transitive relations.
- The poset of relations from $A$ to $B$ is is the subposet $\smash {\mathbf{Rel}^{\mathsf{trans}}\webleft (A\webright )}$ of $\mathbf{Rel}\webleft (A,A\webright )$ spanned by the transitive relations.
